Self-tuning resonant power transfer systems

ABSTRACT

Systems and designs for tuning a wireless power transfer system are provided, which may include any number of features. In one embodiment, a wireless power transfer system can be configured such that resonant frequencies of the system move towards an operating frequency of the system as a coupling coefficient between the transmit and receive resonators becomes smaller. In another embodiment, a receive controller can be configured to control a current delivered to a DC load by comparing an actual current at the DC load to a current requested by the DC load and adjusting an angle or a magnitude of a voltage at the DC load to match the requested current. In another embodiment, a rectifier circuit can act as a controlled voltage source and be configured to tune resonant frequencies between the transmit resonator and the receive resonator. Methods of use are also provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. Non-Provisional patentapplication Ser. No. 15/016,840, filed on Feb. 5, 2016, titled“Self-Tuning Resonant Power Transfer Systems”, which is a continuationof U.S. Non-Provisional patent application Ser. No. 13/953,583, filed onJul. 29, 2013, titled “Self-Tuning Resonant Power Transfer Systems”which claims the benefit of U.S. Provisional Patent Application No.61/676,637, filed on Jul. 27, 2012, titled “Self-Tuning Resonant PowerTransfer Systems”, U.S. Provisional Patent Application No. 61/790,682,filed on Mar. 15, 2013, titled “Self-Tuning Resonant Power TransferSystems”, and U.S. Provisional Patent Application No. 61/676,674, filedon Jul. 27, 2012, titled “Resonant Power Transfer Systems HavingSynchronous Rectification”.

INCORPORATION BY REFERENCE

All publications and patent applications mentioned in this specificationare herein incorporated by reference to the same extent as if eachindividual publication or patent application was specifically andindividually indicated to be incorporated by reference.

FIELD

The field relates generally to resonant wireless power transfer systems,and more specifically to implantable resonant wireless power transfersystems.

BACKGROUND

Many implantable medical devices require electrical systems to power theimplant. Typically, this is achieved using percutaneous wiring toconnect a power source to the implant.

More recently, there has been development into powering an implanteddevice wirelessly with a Transcutaneous Energy Transfer (TET) system,e.g., through an oscillating magnetic field. For a TET system to beuseful, electrical energy storage and processing must be provided whenexternal power is interrupted or not available. This electrical energyprocessing and storage can be implemented with solid-state electronicsand a battery.

Typically, implantable medical devices, such as implanted sensors,require very little power to operate. With such low power levels (on theorder of milliwatts), power transfer levels and efficiency can be lower.With higher power devices (e.g. on the order of watts and up to 15 W ormore), efficient transfer of wireless power is extremely important.Additionally, positions within the body are limited that can accommodatelarger implanted devices, some of which are deep below the skin surface.These implant locations require additional attention to position andorientation of both the transmit and receive coils, as well astechniques to improve and maximize transfer efficiency.

Previous TET systems for implantable medical devices required theimplanted receiver coil to be positioned just under the skin, andtypically include a mechanical feature to align the receive and transmitcoils and keep them together. By implanting these devices directly underthe skin, the size and power requirements of these implanted devices islimited if they are to be powered by a TET system.

SUMMARY OF THE DISCLOSURE

A wireless power transfer system is provided, comprising a transmitresonator coupled to a voltage source and a first impedance matchingnetwork, and a receive resonator coupled to a second impedance matchingnetwork, the receive resonator being inductively coupled to the transmitresonator, the system being configured such that resonant frequencies ofthe system move towards an operating frequency of the system as acoupling coefficient between the transmit and receive resonators becomessmaller.

In some embodiments, resonator tuning between the receiver and transmitresonators is optimized to keep a voltage gain within a specified rangeas the coupling coefficient varies.

In other embodiments, resonator tuning between the receiver and transmitresonators is optimized to maximize efficiency over a given range.

In one embodiment, resonator tuning between the receiver and transmitresonators is optimized to achieve a minimum amount of power transferredfor a given source voltage.

In some embodiments, the system is self-tuning and does not require anexternal control system to operate.

A method of controlling a wireless power transfer system is alsoprovided, comprising the steps of transmitting wireless power from atransmit resonator to a receive resonator, and allowing resonantfrequencies of the system to move towards an operating frequency of thesystem as a coupling coefficient between the transmit and receiveresonators becomes smaller.

A wireless power transfer system is provided, comprising a transmitresonator coupled to a voltage source and a first magnetic impedancematching network, a receive resonator coupled to a second magneticimpedance matching network, the receive resonator being inductivelycoupled to the transmit resonator, a transmit controller coupled to thefirst magnetic impedance matching network, the transmit controllerconfigured to control a current in the first magnetic impedance matchingnetwork to generate a magnetic field in the transmit resonator, and areceive controller coupled to the second magnetic impedance matchingnetwork, the receive controller configured to control a currentdelivered to a DC load by comparing an actual current at the DC load toa current requested by the DC load and adjusting an angle or a magnitudeof a voltage at the DC load to match the requested current.

In some embodiments, the DC load comprises a battery of an implantablemedical device attached to the receive resonator.

In another embodiment, the current requested by the DC load isdetermined by a battery charge algorithm executed on the receivecontroller.

A method of controlling a wireless power transfer system is provided,comprising the steps of transmitting wireless power from a transmitresonator to a receive resonator, and controlling a current delivered toa DC load connected to the receive resonator by comparing an actualcurrent at the DC load to a current requested by the DC load andadjusting an angle or a magnitude of a voltage at the DC load to matchthe requested current.

A wireless power transfer system is provided, comprising a transmitresonator coupled to a voltage source, and a receive resonatorinductively coupled to the transmit resonator and connected to a loadwith a rectifier circuit comprising a plurality of FETs, wherein therectifier circuit acts as a controlled voltage source and is configuredto tune resonant frequencies between the transmit resonator and thereceive resonator.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the invention are set forth with particularity inthe claims that follow. A better understanding of the features andadvantages of the present invention will be obtained by reference to thefollowing detailed description that sets forth illustrative embodiments,in which the principles of the invention are utilized, and theaccompanying drawings of which:

FIG. 1 illustrates a basic wireless power transfer system.

FIG. 2 illustrates the flux generated by a pair of coils.

FIGS. 3A-3B illustrate the effect of coil alignment on the couplingcoefficient.

FIG. 4 illustrates a two-coil system having a transmitter and areceiver.

FIG. 5 shows a four-coil system having a transmitter and a receiver.

FIG. 6 illustrates a voltage gain vs. frequency plot showing the effectof coupling coefficient.

FIG. 7 illustrates one embodiment of a resonant system with magneticimpedance matching networks.

FIG. 8 is a simplified diagram of FIG. 7.

FIG. 9 illustrates one embodiment of a simplified control system.

FIG. 10 illustrates a PI controller for a transmit resonator.

FIG. 11 shows a Thevenin equivalent of the resonators of FIG. 8.

FIG. 12 illustrates a simplified schematic of one portion of a circuitaccording to the invention.

FIG. 13 illustrates a PI controller on the receiver configured tocontrol the DC current.

FIG. 14 shows the Idc current sensor between the output of the MOSFETbridge and the capacitor.

FIG. 15 illustrates a PI controller that can be used to control thevoltage, with the Idcy current controller embedded in the control loop.

FIG. 16 shows one embodiment of a receiver with a passive rectifiercircuit.

FIG. 17 illustrates one embodiment a TET system designed so the outputvoltages from the resonators remain relatively steady with variations incoupling and load.

DETAILED DESCRIPTION

In the description that follows, like components have been given thesame reference numerals, regardless of whether they are shown indifferent embodiments. To illustrate an embodiment(s) of the presentdisclosure in a clear and concise manner, the drawings may notnecessarily be to scale and certain features may be shown in somewhatschematic form. Features that are described and/or illustrated withrespect to one embodiment may be used in the same way or in a similarway in one or more other embodiments and/or in combination with orinstead of the features of the other embodiments.

Various aspects of the invention are similar to those described inInternational Patent Pub. No. WO2012045050; U.S. Pat. Nos. 8,140,168;7,865,245; 7,774,069; 7,711,433; 7,650,187; 7,571,007; 7,741,734;7,825,543; 6,591,139; 6,553,263; and 5,350,413; and U.S. Pub. Nos.2010/0308939; 2008/027293; and 2010/0102639, the entire contents ofwhich patents and applications are incorporated herein for all purposes.

Wireless Power Transmission System

Power may be transmitted wirelessly by magnetic induction. In variousembodiments, the transmitter and receiver are closely coupled.

In some cases “closely coupled” or “close coupling” refers to a systemthat requires the coils to be very near each other in order to operate.In some cases “loosely coupled” or “loose coupling” refers to a systemconfigured to operate when the coils have a significant spatial and/oraxial separation, and in some cases up to distance equal to or less thanthe diameter of the larger of the coils. In some cases, “looselycoupled” or “loose coupling” refers a system that is relativelyinsensitive to changes in physical separation and/or orientation of thereceiver and transmitter.

In various embodiments, the transmitter and receiver are non-resonantcoils. For example, a change in current in one coil induces a changingmagnetic field. The second coil within the magnetic field picks up themagnetic flux, which in turn induces a current in the second coil. Anexample of a closely coupled system with non-resonant coils is describedin International Pub. No. WO2000/074747, incorporated herein for allpurposes by reference. A conventional transformer is another example ofa closely coupled, non-resonant system. In various embodiments, thetransmitter and receiver are resonant coils. For example, one or both ofthe coils is connected to a tuning capacitor or other means forcontrolling the frequency in the respective coil. An example of closelycoupled system with resonant coils is described in International Pub.Nos. WO2001/037926; WO2012/087807; WO2012/087811; WO2012/087816;WO2012/087819; WO2010/030378; and WO2012/056365, and U.S. Pub. No.2003/0171792, incorporated herein for all purposes by reference.

In various embodiments, the transmitter and receiver are looselycoupled. For example, the transmitter can resonate to propagate magneticflux that is picked up by the receiver at relatively great distances. Insome cases energy can be transmitted over several meters. In a looselycoupled system power transfer may not necessarily depend on a criticaldistance. Rather, the system may be able to accommodate changes to thecoupling coefficient between the transmitter and receiver. An example ofa loosely coupled system is described in International Pub. No.WO2012/045050, incorporated herein for all purposes by reference.

Power may be transmitted wirelessly by radiating energy. In variousembodiments, the system comprises antennas. The antennas may be resonantor non-resonant. For example, non-resonant antennas may radiateelectromagnetic waves to create a field. The field can be near field orfar field. The field can be directional. Generally far field has greaterrange but a lower power transfer rate. An example of such a system forradiating energy with resonators is described in International Pub. No.WO2010/089354, incorporated herein for all purposes by reference. Anexample of such a non-resonant system is described in International Pub.No. WO2009/018271, incorporated herein for all purposes by reference.Instead of antenna, the system may comprise a high energy light sourcesuch as a laser. The system can be configured so photons carryelectromagnetic energy in a spatially restricted, direct, coherent pathfrom a transmission point to a receiving point. An example of such asystem is described in International Pub. No. WO2010/089354,incorporated herein for all purposes by reference.

Power may also be transmitted by taking advantage of the material ormedium through which the energy passes. For example, volume conductioninvolves transmitting electrical energy through tissue between atransmitting point and a receiving point. An example of such a system isdescribed in International Pub. No. WO2008/066941, incorporated hereinfor all purposes by reference.

Power may also be transferred using a capacitor charging technique. Thesystem can be resonant or non-resonant. Exemplars of capacitor chargingfor wireless energy transfer are described in International Pub. No.WO2012/056365, incorporated herein for all purposes by reference.

The system in accordance with various aspects of the invention will nowbe described in connection with a system for wireless energy transfer bymagnetic induction. The exemplary system utilizes resonant powertransfer. The system works by transmitting power between the twoinductively coupled coils. In contrast to a transformer, however, theexemplary coils are not coupled together closely. A transformergenerally requires the coils to be aligned and positioned directlyadjacent each other. The exemplary system accommodates looser couplingof the coils.

While described in terms of one receiver coil and one transmitter coil,one will appreciate from the description herein that the system may usetwo or more receiver coils and two or more transmitter coils. Forexample, the transmitter may be configured with two coils—a first coilto resonate flux and a second coil to excite the first coil. One willfurther appreciate from the description herein that usage of “resonator”and “coil” may be used somewhat interchangeably. In various respects,“resonator” refers to a coil and a capacitor connected together.

In accordance with various embodiments of this disclosure, the systemcomprises one or more transmitters configured to transmit powerwirelessly to one or more receivers. In various embodiments, the systemincludes a transmitter and more than one receiver in a multiplexedarrangement. A frequency generator may be electrically coupled to thetransmitter to drive the transmitter to transmit power at a particularfrequency or range of frequencies. The frequency generator can include avoltage controlled oscillator and one or more switchable arrays ofcapacitors, a voltage controlled oscillator and one or more varactors, aphase-locked-loop, a direct digital synthesizer, or combinationsthereof. The transmitter can be configured to transmit power at multiplefrequencies simultaneously. The frequency generator can include two ormore phase-locked-loops electrically coupled to a common referenceoscillator, two or more independent voltage controlled oscillators, orcombinations thereof. The transmitter can be arranged to simultaneouslydelivery power to multiple receivers at a common frequency.

In various embodiments, the transmitter is configured to transmit a lowpower signal at a particular frequency. The transmitter may transmit thelow power signal for a particular time and/or interval. In variousembodiments, the transmitter is configured to transmit a high powersignal wirelessly at a particular frequency. The transmitter maytransmit the high power signal for a particular time and/or interval.

In various embodiments, the receiver includes a frequency selectionmechanism electrically coupled to the receiver coil and arranged toallow the resonator to change a frequency or a range of frequencies thatthe receiver can receive. The frequency selection mechanism can includea switchable array of discrete capacitors, a variable capacitance, oneor more inductors electrically coupled to the receiving antenna,additional turns of a coil of the receiving antenna, or combinationsthereof.

In general, most of the flux from the transmitter coil does not reachthe receiver coil. The amount of flux generated by the transmitter coilthat reaches the receiver coil is described by “k” and referred to asthe “coupling coefficient.”

In various embodiments, the system is configured to maintain a value ofk in the range of between about 0.2 to about 0.01. In variousembodiments, the system is configured to maintain a value of k of atleast 0.01, at least 0.02, at least 0.03, at least 0.04, or at least0.05.

In various embodiments, the coils are physically separated. In variousembodiments, the separation is greater than a thickness of the receivercoil. In various embodiments, the separation distance is equal to orless than the diameter of the larger of the receiver and transmittercoil.

Because most of the flux does not reach the receiver, the transmittercoil must generate a much larger field than what is coupled to thereceiver. In various embodiments, this is accomplished by configuringthe transmitter with a large number of amp-turns in the coil.

Since only the flux coupled to the receiver gets coupled to a real load,most of the energy in the field is reactive. The current in the coil canbe sustained with a capacitor connected to the coil to create aresonator. The power source thus only needs to supply the energyabsorbed by the receiver. The resonant capacitor maintains the excessflux that is not coupled to the receiver.

In various embodiments, the impedance of the receiver is matched to thetransmitter. This allows efficient transfer of energy out of thereceiver. In this case the receiver coil may not need to have a resonantcapacitor.

Turning now to FIG. 1, a simplified circuit for wireless energytransmission is shown. The exemplary system shows a series connection,but the system can be connected as either series or parallel on eitherthe transmitter or receiver side.

The exemplary transmitter includes a coil Lx connected to a power sourceVs by a capacitor Cx. The exemplary receiver includes a coil Lyconnected to a load by a capacitor Cy. Capacitor Cx may be configured tomake Lx resonate at a desired frequency. Capacitance Cx of thetransmitter coil may be defined by its geometry. Inductors Lx and Ly areconnected by coupling coefficient k. Mxy is the mutual inductancebetween the two coils. The mutual inductance, Mxy, is related tocoupling coefficient, k.Mxy=k√{square root over (Lx·Ly)}

In the exemplary system the power source Vs is in series with thetransmitter coil Lx so it may have to carry all the reactive current.This puts a larger burden on the current rating of the power source andany resistance in the source will add to losses.

The exemplary system includes a receiver configured to receive energywirelessly transmitted by the transmitter. The exemplary receiver isconnected to a load. The receiver and load may be connected electricallywith a controllable switch.

In various embodiments, the receiver includes a circuit elementconfigured to be connected or disconnected from the receiver coil by anelectronically controllable switch. The electrical coupling can includeboth a serial and parallel arrangement. The circuit element can includea resistor, capacitor, inductor, lengths of an antenna structure, orcombinations thereof. The system can be configured such that power istransmitted by the transmitter and can be received by the receiver inpredetermined time increments.

In various embodiments, the transmitter coil and/or the receiver coil isa substantially two-dimensional structure. In various embodiments, thetransmitter coil may be coupled to a transmitter impedance-matchingstructure. Similarly, the receiver coil may be coupled to a receiverimpedance-matching structure. Examples of suitable impedance-matchingstructures include, but are not limited to, a coil, a loop, atransformer, and/or any impedance-matching network. Animpedance-matching network may include inductors or capacitorsconfigured to connect a signal source to the resonator structure.

In various embodiments, the transmitter is controlled by a controller(not shown) and driving circuit. The controller and/or driving circuitmay include a directional coupler, a signal generator, and/or anamplifier. The controller may be configured to adjust the transmitterfrequency or amplifier gain to compensate for changes to the couplingbetween the receiver and transmitter.

In various embodiments, the transmitter coil is connected to animpedance-matched coil loop. The loop is connected to a power source andis configured to excite the transmitter coil. The first coil loop mayhave finite output impedance. A signal generator output may be amplifiedand fed to the transmitter coil. In use power is transferredmagnetically between the first coil loop and the main transmitter coil,which in turns transmits flux to the receiver. Energy received by thereceiver coil is delivered by Ohmic connection to the load.

One of the challenges to a practical circuit is how to get energy in andout of the resonators. Simply putting the power source and load inseries or parallel with the resonators is difficult because of thevoltage and current required. In various embodiments, the system isconfigured to achieve an approximate energy balance by analyzing thesystem characteristics, estimating voltages and currents involved, andcontrolling circuit elements to deliver the power needed by thereceiver.

In an exemplary embodiment, the system load power, P_(L), is assumed tobe 15 Watts and the operating frequency of the system, f, is 250 kHz.Then, for each cycle the load removes a certain amount of energy fromthe resonance:

$e_{L} = {\frac{P_{L}}{f} = {60\mspace{14mu}{µJ}\mspace{14mu}{Energy}\mspace{14mu}{the}\mspace{14mu}{load}\mspace{14mu}{removes}\mspace{14mu}{from}\mspace{14mu}{one}\mspace{14mu}{cycle}}}$$e_{L} = {\frac{P_{L}}{f} = {60\mspace{14mu}{µJ}\mspace{14mu}{Energy}\mspace{14mu}{the}\mspace{14mu}{load}\mspace{14mu}{removes}\mspace{14mu}{in}\mspace{14mu}{one}\mspace{14mu}{cycle}}}$

It has been found that the energy in the receiver resonance is typicallyseveral times larger than the energy removed by the load for operative,implantable medical devices. In various embodiments, the system assumesa ratio 7:1 for energy at the receiver versus the load removed. Underthis assumption, the instantaneous energy in the exemplary receiverresonance is 420 μJ.

The exemplary circuit was analyzed and the self inductance of thereceiver coil was found to be 60 uH. From the energy and the inductance,the voltage and current in the resonator could be calculated.

$e_{y} = {\frac{1}{2}{Li}^{2}}$$i_{y} = {\sqrt{\frac{2e_{y}}{L}} = {3.74\mspace{14mu} A\mspace{14mu}{peak}}}$v_(y) = ω L_(y)i_(y) = 352  V  peak

The voltage and current can be traded off against each other. Theinductor may couple the same amount of flux regardless of the number ofturns. The Amp-turns of the coil needs to stay the same in this example,so more turns means the current is reduced. The coil voltage, however,will need to increase. Likewise, the voltage can be reduced at theexpense of a higher current. The transmitter coil needs to have muchmore flux. The transmitter flux is related to the receiver flux by thecoupling coefficient. Accordingly, the energy in the field from thetransmitter coil is scaled by k.

$e_{x} = \frac{e_{y}}{k}$

Given that k is 0.05:

$e_{x} = {\frac{420\mspace{14mu}{µJ}}{0.05} = {8.4\mspace{14mu}{mJ}}}$

For the same circuit the self inductance of the transmitter coil was 146uH as mentioned above. This results in:

$i_{x} = {\sqrt{\frac{2e_{x}}{L}} = {10.7\mspace{14mu} A\mspace{14mu}{peak}}}$v_(x) = ω L_(x)i_(x) = 2460  V  peak

One can appreciate from this example, the competing factors and how tobalance voltage, current, and inductance to suit the circumstance andachieve the desired outcome. Like the receiver, the voltage and currentcan be traded off against each other. In this example, the voltages andcurrents in the system are relatively high. One can adjust the tuning tolower the voltage and/or current at the receiver if the load is lower.

Estimation of Coupling Coefficient and Mutual Inductance

As explained above, the coupling coefficient, k, may be useful for anumber of reasons. In one example, the coupling coefficient can be usedto understand the arrangement of the coils relative to each other sotuning adjustments can be made to ensure adequate performance. If thereceiver coil moves away from the transmitter coil, the mutualinductance will decrease, and ceteris paribus, less power will betransferred. In various embodiments, the system is configured to maketuning adjustments to compensate for the drop in coupling efficiency.

The exemplary system described above often has imperfect information.For various reasons as would be understood by one of skill in the art,the system does not collect data for all parameters. Moreover, becauseof the physical gap between coils and without an external means ofcommunications between the two resonators, the transmitter may haveinformation that the receiver does not have and vice versa. Theselimitations make it difficult to directly measure and derive thecoupling coefficient, k, in real time.

Described below are several principles for estimating the couplingcoefficient, k, for two coils of a given geometry. The approaches maymake use of techniques such as Biot-Savart calculations or finiteelement methods. Certain assumptions and generalizations, based on howthe coils interact in specific orientations, are made for the sake ofsimplicity of understanding. From an electric circuit point of view, allthe physical geometry permutations can generally lead to the couplingcoefficient.

If two coils are arranged so they are in the same plane, with one coilcircumscribing the other, then the coupling coefficient can be estimatedto be roughly proportional to the ratio of the area of the two coils.This assumes the flux generated by coil 1 is roughly uniform over thearea it encloses as shown in FIG. 2.

If the coils are out of alignment such that the coils are at a relativeangle, the coupling coefficient will decrease. The amount of thedecrease is estimated to be about equal to the cosine of the angle asshown in FIG. 3A. If the coils are orthogonal to each other such thattheta (θ) is 90 degrees, the flux will not be received by the receiverand the coupling coefficient will be zero.

If the coils are arranged such that half the flux from one coil is inone direction and the other half is in the other direction, the fluxcancels out and the coupling coefficient is zero, as shown in FIG. 3B.

A final principle relies on symmetry of the coils. The couplingcoefficient and mutual inductance from one coil to the other is assumedto be the same regardless of which coil is being energized.M _(xy) =M _(yx)

Systems and methods are provided herein for wirelessly transmittingpower from an external power transmitter to a separate power receiver.The TET systems described herein can be configured to wirelesslytransmit power from a transmitter positioned outside of a human body toa receiver implanted within the body. The receiver can be coupled tocircuitry and a power source to power and operate an implantable medicaldevice coupled to the receiver.

In some embodiments, the resonant systems described herein can operateat high voltages (possibly greater than 1000 Vac rms) to transmit thehigh power levels required by some implantable applications. Forexample, power levels of as high as approximately 15 W or more aretypically required for a fully implanted LVAD system. In theseembodiments, a voltage divider can be used in the TET system so that theload of the receiver resonator and power source of the transmitterresonator can operate at a lower voltage than other parts of the LVADsystem. The voltage of the driving circuit and load can be dictated by abattery pack, which is typically in the range of 12-20 Vdc. Thisdisclosure describes various embodiments on how this can be implementedin a TET system.

In one embodiment, a voltage divider is formed from capacitors, as shownin FIG. 4. Another embodiment divides down the voltage of system 200with a transformer circuit, as shown in FIG. 5. There can be manyvariations on these circuits that all behave similarly. For instance theinductors in the capacitor divider circuit shown in FIG. 1 can beconfigured such that they have some mutual coupling. This would be ahybrid of the two circuits. It is also possible to mix the circuits usedfor the receiver and the transmitter such that the transmitter has oneconfiguration and the receiver has another.

In a first embodiment, shown in FIG. 4, a TET system 100 comprises tworesonant systems, a transmitter resonator 102 and a receiver resonator104. Each of the resonant systems can be connected to a voltage dividercircuit. Transmitter resonator 102 includes an inductor Lx and acapacitor Cx2 configured as a tank circuit. Receiver resonator 104includes an inductor Ly and a capacitor Cy2 configured as a tankcircuit. In order to excite each resonant system an impedance matchingcircuit can connect the transmitter resonator to the power source andthe receiver resonator to the load. This way the load and power sourceonly have to supply the real part of the power, and the reactive part ofthe power is handled by the impedance matching circuit.

In FIG. 4, the impedance matching circuits can comprise voltage dividersformed from capacitors. Voltage divider 106 can be coupled totransmitter resonator 102 and can comprise capacitor Cx1 and inductorLs, coupled to voltage source Vs. Voltage divider 108 can be coupled toreceiver resonator 104 and can comprise capacitor Cy1 and inductor L1,coupled to the Load. An additional inductor may be needed in series withthe source and load. In a practical circuit the source is most likely aFET push pull circuit operating as a square wave voltage source. Theoutput of the voltage source should not be placed directly across acapacitor or there will be extremely large currents on the switchingtransitions.

Many drive circuits are possible in addition to the FET push pullcircuit (class-D amplifier). These include variations on resonant poweramplifiers (classes B, C, and E) or self resonant circuits such as aRoyer oscillator. Linear amplifiers (classes A and A-B) will also work,but will have lower efficiency.

In a second embodiment of TET system 200, shown in FIG. 5, transmitterresonator 202 includes an inductor Lx2 and a capacitor Cx2 configured asa tank circuit. Receiver resonator 204 includes an inductor Ly2 and acapacitor Cy2 configured as a tank circuit. The impedance matchingcircuits can comprise transformer circuits. Transformer circuit 210 canbe inductively coupled to transmitter resonator 202 and can includecapacitor Cx1 and inductor Lx1 coupled to voltage source Vs. Transformercircuit 212 can be inductively coupled to receiver resonator 204 and cancomprise capacitor Cy1 and inductor Ly2, coupled to the Load.

In FIG. 5, the two coils on the transmitter can act like a transformerso that the voltage on Lx1 is much smaller than the voltage on Lx2. Lx2and Cx2 make up the transmitter resonator, and Lx1 and Cx1 act as anexciter to keep the resonance going.

Both variations described in FIGS. 4 and 5 can be designed to workequally well. There will be trade-offs relating to the details of each,but the advantages and disadvantages will be specific to a particularimplementation. In some embodiments, it is possible to combine thecircuits; for example, the transmitter receiver could utilize theimpedance matching circuit of FIG. 4, and the receiver transmitter couldutilize the impedance matching circuit of FIG. 5.

One aspect of this disclosure is to tune the resonant circuits to makethe circuit relatively insensitive to the relative position andalignment of the transmitter and receiver coils. The percentage of fluxcoupling the transmitter and receiver resonators is referred to as thecoupling coefficient or Previous TET systems have required a large valueof k. The embodiments described above in FIGS. 4 and 5 are relativelyinsensitive to k and will work well down to small values. This isimportant as the transmitter and receiver are placed farther apart, andmay not be well aligned.

The main parameters of a resonant system that are addressed in thisinvention are the power efficiency (e.g., the ratio of the input powerto the output power), and the voltage gain (e.g., the input supplyvoltage to the output voltage). The circuit can be designed, choosingappropriate values of inductances, mutual inductances, and capacitances,to have specific resonant frequencies that vary as a function ofcoupling coefficient. The systems described above optimize theseparameters by being designed such that the resonant frequency of thetransmitter and receiver changes based on the coupling coefficient. As kgets smaller the resonant frequencies of the resonators both get closerto the operating frequency. As the resonant frequency of the resonatorsgets closer to the operating frequency, the voltage gain increases.Typically, as the transmitter and receiver get moved farther apart thevoltage at the receiver will drop. However, according to embodiments ofthis disclosure, as the resonant frequencies converge the voltage gainis improved, which can counteract the voltage drop caused by increaseddistance. The effect achieved by designing the resonant system to havethis characteristic results in a TET system in which an automaticcontrol system is not needed. The circuit is essentially self-tuning.

There are several possible configurations possible for the impedancematching network. These are all can be tuned to provide similarperformance. The preferred circuit topology will be dictated by otherconcerns, such as practical aspects of winding coupled coils, andconstruction of inductors.

The resonant systems described herein can have several resonantfrequencies. In one embodiment, an eighth order system is considered.The system can have four resonant frequencies, or eight complex eigenvalues. The eigen values of the system can be dependent on all theparameters of the system such as the inductor and capacitor values aswell as the coupling coefficient between the coils. As any of theseparameters change, the resonant frequencies will change. The circuit canbe configured such that two of the resonant frequencies will move closerto the operating frequency as the coupling coefficient gets smaller.This behavior can be designed into a circuit that is fourth order orgreater; an eighth order circuit is considered here because it isconvenient for the design of the impedance matching networks. Thisbehavior is determined by the component values used in the circuit.Finding the component values that result in this behavior is verydifficult to do analytically. For the circuit examples described herethe component values were found using iterative numerical analysistechniques.

The separation of the resonant frequencies is shown in FIG. 6, showingthe effect of a changing k on voltage gain vs. frequency. The peaks ofthe voltage gain move farther apart as k gets larger. For example, aresonant system with a k of 0.15 in FIG. 6 shows two peaks of voltagegain at a frequency of approximately 2.8 and 3.2×10⁵ Hz. A smaller kvalue of 0.10 shows two peaks of voltage gain closer together (at 2.9and 3.1×10⁵ Hz), but with a larger voltage gain than with the k value of0.15. Similarly, a k value of 0.05 shows a single, larger peak ofvoltage gain at the operating frequency of 3×10⁵ Hz.

The resonators tuning can also be optimized to keep other parameterswithin a given range. Possible other parameters in addition to voltagegain include efficiency, and the power handling capability for a givensource voltage. This system of this embodiment is self-tuning, thereforeit does not require an external control system to operate. It can bedesigned to operate without a microcontroller continuously tuning thecircuit. Prior implementations have required the circuit to be tuned onthe fly, and require a sophisticated control system.

FIG. 16 illustrates one embodiment of a receiver 604 in a TET system. Inthis system, the receiver resonator 605 is coupled to a load via apassive (diode) rectifier 606 and a voltage regulator 608. The passiverectifier can convert alternating current in the receiver to directcurrent, which can then be delivered to the voltage regulator tomaintain a constant voltage level on the load.

FIG. 17 illustrates one embodiment of an exemplary TET system 400including transmitter 402 and receiver 404, the system being designed sothe output voltages from the resonators remain relatively steady withvariations in coupling and load. Transmitter 402 can comprise a voltagesource and a resonant circuit, such as an inductor Lx and a capacitorCx. Receiver 404 also includes an inductor Ly and a capacitor Cy, andfurther comprises a rectifier circuit 406 coupling the receiver to theload. In the embodiment shown in FIG. 17, the rectifier circuit 406 atthe receiver can be made up of FETs 418 which can be controlled to forma circuit functioning as a synchronous rectifier, in contrast to thepassive diode rectifier circuits commonly used and shown in FIG. 16.This synchronous rectifier of FIG. 17 can be configured to minimize thevoltage drop across the rectifier and improve the efficiency of thecircuit.

In FIG. 17, setting up the rectifier circuit 406 as a full bridge modelsthe receiver as a controlled voltage source. The voltage source iscapable of either sinking or sourcing power. As a receiver, it willnormally be sinking power. If the phase of the voltage source iscontrolled, it can make the load on the system appear reactive. Thereactance of the load can be used to help tune resonant frequencies inthe power transfer resonators. Essentially, it can act as a variablecapacitor.

Thus, power through the system 400 can be controlled by varying themagnitude and phase of either or both of the two voltage sources, eitherVs of the transmitter or the rectifier circuit of the receiver.Additionally, power transmission in the system can be controlledentirely by the receiver, by controlling the rectifier circuit 406 tochange the apparent phase/output of the load. If transmitter voltage isfixed, then receiver can control power flow by varying voltage and phaseof the rectifier circuit.

Additionally, if the duty cycle of the FET bridge rectifier circuit 418is controlled, the bridge can work as a boost converter in one stage, asopposed to the two-stage process shown in FIG. 16 (diode bridge followedby a voltage regulator). This eliminates the need for a second stagethat does the voltage regulation. The boost converter uses the impedanceof the resonator as the inductor of a switching regulator, so the needfor an additional inductor is eliminated.

If the FETs in the rectifier are controlled, the phase of the load doesnot necessarily have to line up with the phase of the current. Operationof the FETs can change the power factor of the load and can make theload look more inductive or capacitive. Operation of the FETs can beused to change the tuning of the resonance and to control how much poweris being delivered.

By setting up the FETs in the load rectifier as a full bridge, therectifier circuit essentially acts as a controlled voltage source. Thismake the system look like a voltage source at the transmitter, and avoltage source at the receiver, connected by an impedance made up of theresonant system. The power flow through the system can be controlled byvarying the magnitude and phase of the two voltage sources relative toeach other. If the transmitter voltage source is fixed, then thereceiver can control the power flow by varying the voltage and phase ofits voltage source, the active rectifier.

In one embodiment, the FETs can be controlled using receiver phasecontrol. If the rectifier circuit 406 of receiver 404 is set up to doactive rectification, it will need to be operating synchronously to thetransmitter. The switching of the MOSFETs controls the receiver voltage,which will need to be phase locked with the current.

There are at least a couple ways to control the switching. A firstmethod drives each side of the bridge with a square wave, the relativephase of the two side determines the effective voltage. The receiverwill need to be able to sense the AC current, and run a phase lockedloop to synchronize the MOSFET switching. A second method is to controldrive each side of the bridge with a center aligned, pulse widthmodulated signal. The two sides can be 180 degrees out of phase. Theduty cycle determines the effective voltage at the bridge. Thesetechniques can be implemented in software running a microcontroller, orin analog hardware.

Since the system is typically running at a couple hundred kHz, the PWMperipheral of the processor will have limited resolution, both forcontrolling the output period and controlling the output duty cycle.This will result in significant jitter due to quantization. This can besmoothed out using sigma-delta modulation techniques.

The power can be controlled to the point where it is even possible forthe load power to be negative, so the receiver is transmitting power.This circuit is similar to using the impedance of the resonator to bethe inductor in a switching regulator.

In another embodiment, a TET system can include magnetically coupledresonant L-C circuits configured to pass energy from a transmitter to areceiver. The magnetically coupled systems described herein can beimplemented in a way so as to maximize system efficiency under a broadrange of operating conditions. FIG. 7 illustrates one embodiment of aTET system 700 having a magnetically coupled impedance matching network.System 700 can include a transmitter resonator 702 and a receiverresonator 704. These two circuits can be excited by magnetic impedancematching circuits 710 and 712, respectively, which can connect thetransmitter resonator 702 to the power source and the receiver resonator704 to the load. A controller or microcontroller can be coupled to thetransmitter and/or receiver, as shown.

In FIG. 7, the DC voltage source 714 and MOSFET bridge 716 can bemodeled as a controlled AC voltage source. The magnitude of the voltagesource can be controlled by controlling the duty cycle of the MOSFETswitching. This magnitude is a phasor voltage Vx. For this analysis theangle of this voltage source is used as the reference for all the phasorangles in the system.

The resonant system illustrated in FIG. 7 is an 8^(th) order L-Ccircuit. The system should include enough damping to dampen out thenatural response quickly relative to the sample rate of the discretetime control system. This way only the forced response of the systemneeds to be considered. In some embodiments, the circuit can be operatedat 250 kHz, and the control loop can run at approximately 1 kHz. Onewill appreciate from the description herein that these principles can beapplied to a broad range of operating frequencies. For example, thesystem can be designed to run at frequencies between about 100 kHz andabout 20 MHz.

The resonant system of FIG. 7 can be represented by a black box two portnetwork. If “A” parameters are used, this is described as:

$\begin{bmatrix}{Vx} \\{Ix}\end{bmatrix} = {\begin{bmatrix}A & B \\C & D\end{bmatrix} \cdot \begin{bmatrix}{Vy} \\{- {Iy}}\end{bmatrix}}$

All the terms in the two port network are phasors. In one embodiment,the operating frequency can be 250 kHz. The parameters of the two portsystem are functions of the coupling coefficient between the coils inthe transmitter and receiver resonators. As the coils are physicallymoved with respect to each other, the coupling coefficient will change,causing the parameters of the two port network to change. In someembodiments, the capacitors in the system (such as the capacitors inresonators 702 and 704 of FIG. 7) can be variable. This offers anotherdegree of freedom for tuning the circuit, however for purposes ofdiscussion the capacitors in this particular system are assumed to befixed values.

Referring still to FIG. 7, the MOSFET bridge 718 on the receiver ismodeled as an AC voltage source. In normal operation this voltage sourcewill be sinking power. The power can be converted to a DC voltage. Forthis analysis the bridge is assumed to be 100% efficient, so givenconservation of power, the AC power absorbed by the AC voltage source isconverted into the DC power produced by the DC voltage source.

Given these simplifications the system can be modeled as shown in FIG.8. The system 800 of FIG. 8 is divided into two halves, the transmitter802 and receiver 804. The receiver can be connected to a load 806. Theinformation that can be communicated between the transmitter andreceiver is very limited. For simplification it is assumed there is nocommunication between the transmitter and receiver. This means there canbe a control system or controller on the transmitter side and a separatecontrol system or controller on the receiver side that are workingindependently and are only coupled through interactions with the plant:the resonant system.

On the transmitter 802 side the magnitude of the voltage Vx can becontrolled with a controller in the transmitter to get a desired Ix.Since the angle of the voltage Vx is used as the angle reference for thesystem, the magnitude of the voltage is the only value that can bemanipulated. The goal is to get a large Ix resulting in a large magneticfield in the resonant system so the range of the system is as large aspossible.

On the receiver 804 side the AC voltage source Vy can be varied with acontroller in the receiver. Both the magnitude and phase angle can bemanipulated. The goal of controlling this is to control either Vdcy orIdcy depending on how the load 806 is configured. If the resonators arecoupled to an implanted medical device, such as an LVAD, the load can bea battery and a pump. In this example, the DC voltage is the batteryvoltage, and Idcy is controlled to charge the battery. The value of Idcycan be controlled according to a battery charge algorithm executed bythe controller on the receiver. On very rare occasions a battery faultcan result in the battery being disconnected from the DC bus. Underthese conditions the DC bus voltage needs to be controlled.

A generalized control system 901 can be represented as shown in FIG. 9.Cx is a generic control law that adjusts the transmitter voltage Vx toachieve a desired transmitter current, Ix. Cy is a generic control lawthat adjust the phase angle θ of the receiver voltage to achieve adesired DC bus current, Idcy. P represents the plant, this is the systemshown in FIG. 8. There are many possible control schemes that can beused for Cx and Cy. A common implementation would use a PID controller.The control system can be implemented in firmware running on twocontrollers or microcontrollers, one in the transmitter and one in thereceiver. Thus, in some embodiments there are two control systems, onein the transmitter and one in the receiver, both acting on the sameresonant system. The electronic hardware in the system can have outputsthat can control the switching of the MOSFET bridges in both thetransmitter and receiver. The switching can control the voltagemagnitude, frequency or phase of the voltage on the AC side of thebridges, V_(x)∠0 and Vy∠θ as shown in FIGS. 7 and 8. The hardware canalso have sensors to measure the currents in system, I_(x)∠α andI_(y)∠β. The part of the control system implemented in the transmitter(e.g., the transmitter of FIGS. 7-8) is configured to adjust themagnitude of Vx to drive Ix to a specific value. The part of the controlsystem implemented in the receiver (e.g., the receiver of FIGS. 7-8) isconfigured to adjust the phase angle of the rectifier voltage to driveIdcy to a specified value. The details of the actual control systems aremore complicated.

The goal of the transmitter controller is to run a large current in thetransmitter resonator in order to get a large magnetic field. Increasingthe size of the magnetic field maximizes the range of the resonatorsystem. The controller for the transmitter can be a relatively simple PIcontroller shown in FIG. 10. In one embodiment, the controller observesthe magnitude of the current in the transmitter exciter winding, Ix,compares it to a desired reference point, Ix*. The error between thedesired current and the actual observed current is used to turn theoutput voltage Vx up or down until the actual current matches thedesired current. The output voltage command, Vx corresponds to the dutycycle of the MOSFET bridge 716 from FIG. 7.

In practice, the input impedance of the resonant system is frequentlyhigh enough that the transmitter is running at its maximum outputvoltage. The integrator in the transmitter control loop needs a clamp toprevent windup. The control system 1001 in FIG. 10 is configured toprevent windup of the system at high or maximum output voltages.

The MOSFET bridge (716 from FIG. 7) controlling the AC voltage source Vxis limited by the source DC bus voltage. The duty cycle can only go upto 100%. For some resonant systems this may be limited to a ⅔ dutycycle. The actual output of the MOSFET bridge is a square wave whichwill have higher order odd harmonics. A ⅔ duty cycle will result in avoltage wave form with no 3^(rd) harmonic or multiples of the 3^(rd)harmonic. This is useful to avoid distortion of the waveform if theresonant system has eigen values that fall close to the 3^(rd) harmonic,750 kHz.

The receiver control is more complicated. To start with, a slightlybetter model of the plant needs to be developed. The resonant system ismodeled looking at the receiver side only. A Thevenin equivalent 805 ofresonators 802 and 804 of FIG. 8 is shown in FIG. 11. The Theveninequivalent voltage is usually much larger than Vy, and the equivalentimpedance is relatively large. As a result this can be approximated as acurrent source driving Iy as shown in FIG. 12.

The MOSFET bridge of the receiver, item 718 from FIG. 7, can be modeledas an AC voltage source coupled to a DC voltage source. In this modelthe two voltage sources represent the MOSFET bridge as seen from the DCside and from the AC side. The two sides are linked so that the powerflowing into one side equals the power flowing out of the other side.More specifically, the voltage sources of the transmitter and receiverare coupled such that the real power flowing into one is the same as thereal power flowing out of the other. This assumes 100% efficiency, whichfor these purposes is a reasonable approximation.

The power relationship can be expressed as:

Re{−Iy^(*) ⋅ Vy} = Idc ⋅ VdcRe{Iy ⋅ (Vy ⋅ cos (θ − β + π) + j ⋅ sin (β − θ))} = Idc ⋅ VdcIy ⋅ Vy ⋅ cos (θ − β + π) = Idc ⋅ Vdc${Idc} = {{Iy}\frac{Vy}{Vdc}{\cos( {\theta - \beta + \pi} )}}$

Referring back to FIG. 8, the angle of the transmitter voltage can bearbitrarily picked as the reference, so θ can be the angle of thereceiver voltage relative to the transmitter voltage, and β can be theangle of the receiver current relative to the transmitter voltage. Tocontrol the receiver, the difference between θ and β is important. Inthe last expression, Iy is an input to the system that is a function ofthe operating condition of the resonators and the transmitter current.The term

$\frac{Vy}{Vdc}$is proportional to the duty cycle of the MOSFET bridge of the receiver,this is expressed as Kd. The angle (θ−β) is the difference in the angleof the current and the voltage. The π occurs in the cos in order to makethe magnitude of the equation positive. In order to control the DCcurrent the receiver can control either θ or the duty cycle. In thisdesign, the duty cycle is fixed and the phase angle is the controlleroutput of the voltage, θ.

To control the DC current, a PI controller can be used, as shown in FIG.13. The PI controller 1300 observes the difference between the requestedcurrent and the actual current and adjusts θ, the angle of the voltage,in order to drive Idcy to match the requested value. In FIG. 13 the gainblock Kii and Kpi are the proportional and integral gains, the extra ‘i’in the subscript is notation to indicate these are gains for controllingthe current. The greyed out section of FIG. 13 represents the plantusing the approximate model derived above.

A minor refinement to the basic PI controller is to add a factor of

$\frac{1}{Iy}$to the forward path. Iy is measured by the controller, and adding thisterm keeps the loop gain constant as Iy changes due to conditions in theresonator. The stability of the control loop is a function of all thegains in the loop. Iy shows up as a gain in this loop, so stability overa broad range of conditions can be improved by correcting for Iy.

It should be noted that the integrator in FIG. 13 does not have a clampsince its output is an angle, so rather than saturating, the outputangle wraps around in a circle. The angle of the current β is ultimatelydriven by the transmitter. Since the clocks of the transmittercontroller and the receiver controller are not synchronous, β will beslowly drifting around with respect to the reference in the receiver dueto the difference between the clock on the transmitter and the clock onthe receiver. Letting the integrator wrap around allows the receiver totrack this drift.

In the rare case where the battery is not connected, the TETS systemneeds to be able to control the DC bus voltage. To accomplish this, avoltage control loop is wrapped around the current controller. To helpwith the stability of the controller a capacitor can be used on the DCbus. The Idc current sensor is between the output of the MOSFET bridgeand the capacitor. This is shown in FIG. 14.

The voltage on the bus is a function of the capacitor current(Idcy−Iload). For a given sample period, Ts, the bus voltage is:

${{Vdcy}(t)} = {\int_{\;}^{\;}{\frac{( {{Idcy} - {Iload}} )}{C}{dt}}}$${{Vdcy}(z)} = \frac{( {{Idcy} - {Iload}} ) \cdot {Ts}}{( {1 - z^{- 1}} ) \cdot C}$

In FIG. 15, a simple PI controller can be used to control the voltage,with the Idcy current controller, from FIG. 13, embedded in the controlloop. This wraps a voltage control loop around the current control loopto regulate the DC bus voltage. The load current is modeled as adisturbance that the control loop act to reject to keep the DC busvoltage constant. The capacitor on the bus is required in order to keepthe control loop stable. The larger the capacitance the easier it is tokeep the loop stable.

As for additional details pertinent to the present invention, materialsand manufacturing techniques may be employed as within the level ofthose with skill in the relevant art. The same may hold true withrespect to method-based aspects of the invention in terms of additionalacts commonly or logically employed. Also, it is contemplated that anyoptional feature of the inventive variations described may be set forthand claimed independently, or in combination with any one or more of thefeatures described herein. Likewise, reference to a singular item,includes the possibility that there are plural of the same itemspresent. More specifically, as used herein and in the appended claims,the singular forms “a,” “and,” “said,” and “the” include pluralreferents unless the context clearly dictates otherwise. It is furthernoted that the claims may be drafted to exclude any optional element. Assuch, this statement is intended to serve as antecedent basis for use ofsuch exclusive terminology as “solely,” “only” and the like inconnection with the recitation of claim elements, or use of a “negative”limitation. Unless defined otherwise herein, all technical andscientific terms used herein have the same meaning as commonlyunderstood by one of ordinary skill in the art to which this inventionbelongs. The breadth of the present invention is not to be limited bythe subject specification, but rather only by the plain meaning of theclaim terms employed.

What is claimed is:
 1. A wireless power transfer system comprising: atransmitter comprising a transmit resonator coupled to a voltage source;and a receiver comprising a receive resonator, a load, a rectifiercoupled between the receive resonator and the load and comprising aplurality of field effect transistors (FETs), and a receiver controllerconfigured to control the plurality of FETs to tune a resonance of thewireless power transfer system.
 2. The wireless power transfer system ofclaim 1, wherein the receiver controller is configured to control a dutycycle of the plurality of FETs to cause the rectifier circuit to operateas a single stage boost converter.
 3. The wireless power transfer systemof claim 1, wherein the receiver controller is configured to control theplurality of FETs by driving each side of the rectifier circuit with asquare wave.
 4. The wireless power transfer system of claim 1, whereinthe receiver controller is configured to control the plurality of FETsby driving each side of the rectifier circuit with a center aligned,pulse width modulated signal.
 5. The wireless power transfer system ofclaim 4, wherein the pulse width modulated signal on a first side of therectifier circuit is 180 degrees out of phase with the pulse withmodulated signal on a second side of the rectifier circuit.
 6. Thewireless power transfer system of claim 1, wherein the receivercontroller is configured to: detect an alternating current through thereceive resonator; and run a phase locked loop to synchronize switchingof the plurality of FETs.
 7. The wireless power transfer system of claim1, wherein the transmitter further comprises a metal-oxide-semiconductorfield-effect transistor (MOSFET) bridge coupled between the transmitresonator and the voltage source, wherein the voltage source and theMOSFET bridge form a controlled AC voltage source, and wherein a voltageof the controlled AC voltage source is controllable by modifying aswitching duty cycle for the MOSFET bridge.
 8. The wireless powertransfer system of claim 1, wherein the receiver further comprises acurrent sensor coupled to an output of the rectifier circuit.
 9. Thewireless power transfer system of claim 1, wherein the receivercontroller comprises a current sensor configured to measure an ACcurrent through the receive resonator.
 10. The wireless power transfersystem of claim 1, wherein the load is a battery, wherein the rectifiercircuit is configured to output a DC current, and wherein the receivercontroller is configured to control the DC current according to abattery charge algorithm.
 11. The wireless power transfer system ofclaim 1, wherein the receiver controller is configured to control theplurality of FETs based on a difference between an angle of a receivervoltage and an angle of a receiver current.
 12. The wireless powertransfer system of claim 1, wherein the receiver controller is aproportional-integral controller.
 13. The wireless power transfer systemof claim 12, wherein the proportional-integral controller incorporates afactor of an inverse of a current through the receive resonator to keepa loop gain constant as the current through the receive resonatorchanges.
 14. A wireless power transfer system comprising: a transmittercomprising a transmit resonator, a voltage source, ametal-oxide-semiconductor field-effect transistor (MOSFET) bridgecoupled between the transmit resonator and the voltage source, and atransmitter controller configured to control switching of the MOSFETbridge; and a receiver comprising a receive resonator coupled to a load.15. The wireless power transfer system of claim 14, wherein thetransmitter controller is a proportional-integral controller comprisingan integrator.
 16. The wireless power transfer system of claim 15,wherein the integrator is clamped to prevent windup at high outputvoltages.
 17. The wireless power transfer system of claim 14, whereinthe transmitter further comprises a transmitter exciter winding, andwherein the transmitter controller is further configured to: measure acurrent through a transmitter exciter winding; compare the measuredcurrent to a desired reference current; and adjust an output voltage ofthe transmitter until the measured current matches the desired referencecurrent.
 18. A method of operating a wireless power transfer system, themethod comprising: inductively coupling a transmitter to a receiver, thetransmitter including a transmit resonator coupled to a voltage source,and the receiver including a receive resonator, a load, a rectifiercoupled between the receive resonator and the load and including aplurality of field effect transistors (FETs), and a receiver controller;and controlling, using the receiver controller, the plurality of FETs totune a resonance of the wireless power transfer system.
 19. The methodof claim 18, wherein controlling the plurality of FETs comprisescontrolling a duty cycle of the plurality of FETs to cause the rectifiercircuit to operate as a single stage boost converter.
 20. The method ofclaim 18, wherein controlling the plurality of FETs comprisescontrolling the plurality of FETs by driving each side of the rectifiercircuit with a square wave.